In conventional electron beam lithography, when a desired pattern is exposed using electron beam, compensations for a proximity effect between exposed patterns (inter-proximity effect) and a proximity effect within a pattern (intra-proximity effect) are, in advance, conducted.
In this regard, correction methods, such as Ghost method (G. Owen et al., J. Vac. Technol. B3, 153(1985)) and self-consistent method (M. Parikh, J. Appl. Phys. 50, 4371(1979)), are generally used.
To quantify the proximity effect, exposure intensity distribution (EID) function (T. H. P. Chang, J. Vac. Sci. Technol. 12, 1271(1975)), which is given by summing two Gaussian distributions as shown in expression (1), is used. EQU f(r)=1/(1+.eta.).pi.*[1/.beta.f.sup.2 *exp(-r.sup.2 /.beta.f.sup.2)+.eta./.beta.b.sup.2 *exp(-r.sup.2 /.beta.b.sup.2) (1)
The first item of expression (1) (EID function) represents an energy distribution accumulated when electron (incident electron beam 20) addressed to the resist 2 penetrates thereinto while forward-scattering, and the second item of expression (1) represents an energy distribution accumulated when electron (incident electron beam 20) is, as shown by arrows 23, backward-scattered by the atomic nucleus in the resist 2 and base substrate 22 in the direction reverse to the incident direction.
Meanwhile, in expression (1), ".beta.f" is called "forward-scattering diameter (standard deviation of Gaussian distribution at the first item)", ".beta.b" is called "backward-scattering diameter (standard deviation of Gaussian distribution at the second item)", and ".eta." is called "backward-scattering ratio (the coefficient of energy accumulated by backward scattering and energy accumulated by forward scattering)". The constants, ".beta.f", ".beta.b" and ".eta." are generally obtained by a computer simulation, where the shield Rutherford scattering formula and Bethe energy loss formula are used [M. Parikh and D. F. Kyser, J. Appl. 50, 1104(1979)].
Especially, the backward-scattering coefficient ".eta." of the above constants is dependent on the base substrate 22 and is generally determined by atomic weight, density and film thickness of only a base material to be etched after exposure.
Proximity effect compensation methods used typically are based upon the above-mentioned proximity effect compensation methods. However, they cause a decrease in exposure throughput and a long-time operation in correction calculation as ULSI with finer-structure and higher-density has been recently developed.
Further, although the dimension accuracy is required to be less than 10% of a designed dimension, there can occur a lack of dimension accuracy in the typical correction methods.
Japanese patent application laid-open Nos. 5-160010(1993) and 8-37146(1996) disclose simplified correction methods to overcome a decrease in exposure throughput and a long-time operation in correction calculation.
In these methods, a drawing area is, in advance, obtained for each region with an arbitrary size to given patterns, then a supplemental exposure by using a quantity of exposure dependent on the area is conducted, the proximity effect between desired exposure patterns is equalized, and a desired pattern is exposed with decrease by the quantity of the supplement exposure.
However, the lack of correction dimension accuracy cannot be solved even by these methods since they are based on the compensation of the intershape proximity effect and intrashape proximity effect.
As described above, the conventional proximity effect correction methods used when conducting the exposure using electron beam are based on only the compensation of the intershape proximity effect and intrashape proximity effect. Namely, they do not take the influences (energy accumulation due to backward scattering) of a base substrate structure with complicated arrangement and shape already provided into account.
Furthermore, even when an overlay exposure by using electron beam is conducted in a process for complicated base structure, such as a wiring process, the influences of the base substrate are not taken into account. Thus, it causes a reduction in resist dimension accuracy after the exposure.
The causes of the accuracy reduction will be detailed below.
In the EID function (represented by expression (1)) to be used when calculating the proximity effect correction, the influences of the base structure (energy accumulation due to backward scattering) is estimated by the second item of expression (1).
The backward-scattering diameter ".beta.b" and the backward-scattering coefficient ".eta." in the second item are constants to determine the quantity of accumulated energy due to backward scattering. However, these constants are provided based on that influences of base structure are equal. Thus, a complicated structure, a shape and an arrangement of pattern, a kind of film material etc. already formed cannot be taken into account.
Especially when metal wirings overlapped several layers are exposed overlaying on a base layer already formed, the reduction of dimension accuracy in the resist pattern obtained by conducting the conventional proximity effect correction becomes significant.
Recently, dimension accuracy less than 0.020 .mu.m, that corresponds to 10% of design dimension less than 0.20 .mu.m, is needed with the developing of higher-density and finer-structure device. Therefore, it is indispensable to avoid the lack of proximity effect correction to base layer that may cause the reduction of dimension accuracy.